How to state the equations of a rational functions with the following asymptotes?

(1)x=2, y=-3

(2)y=0, x=4

(3)y=0

Welcome NYH,
It's not clear what you ask. There can be several rational functions with two common asymptotes & the classification would be difficult.
The simplest curve for {x=h,y=k} would be the hyperbola (x-h)(y-k) =1.
For (3) , y=0 itself is the simplest.